RKKY interaction corresponds to an indirect coupling mechanism of nuclear magnetic moments or localized inner d- or f-shell electron spins in a metal by means of an interaction through the conduction electrons. RKKY interaction This intecation ican be treated by second-order perturbation theory. Its range is ~1/x^4 and it can be used to explain the giant magnetoresistance (GMR) phenomena.

In particular, in magnetic multilayers, because of the RKKY interaction, the coupling changes its sign from one layer to another, giving rise to a succession of ferro and antiferro layers and the "spin valve" phenomenon.

Astonishing Dear Prof. Mohamed El Hafidi, thank you so much for your post.

I didn't know that RKKY interaction can explain the giant magnetoresistance effect, I think it was discovered in the 90s.

Also from your post, I understand that the RKYY interaction depending on the j sign can map a ferromagnet antiferromagnet phase diagram. Thank you.

RKKY (Ruderman - Kittel - Kasuya- Yosida interaction is the coupling via conduction electrons. As the behavior of conduction electrons near the fermi surface is wave -like many types of magnetic ordering may appear as a result of RKKY interaction, for example spiromagnetism, modulated magnetism, and even the spin glass coupling may be accounted by the RKKY interactions. As the interaction is oscillating and decreases as x^-4 the distance between the spins in determinant of the kind of magnetic coupling

Thank you so much for your post, Dear Prof. Jose Roberto Iglesias.

Very interesting to know that the wave-like behaviour of itinerant electrons near the FS, can be modelled by the RKKY interaction.

In addition, thank you for pointing out that the magnetic coupling via conduction electrons helps to explain spiromagnetism, modulated magnetism, and even the spin-glass behaviour since as you pointed out, the RKKY interaction is oscillating and decreases as 1/x4, being the distance between the spins x, a determinant of the kind of magnetic coupling.

P. Contreras: Indeed, the wave like behavior is a consequence of the Fermi surface being sharp and this is at the origin of the RKKY interaction. RKKY is a consequence of the wave-like behavior.

Sorry, does sharp FS means, it is a corrugated FS surface, Dear Prof. Jose Roberto Iglesias?

One aspect of this problem can be found in the review: A.L. Kuzemsky, Unconventional and Exotic Magnetism in Carbon-Based Structures and Related Materials \\ International Journal of Modern Physics B (IJMPB), Volume: 27, Issue: 11 (2013) p.1330007 (40 pages), DOI: 10.1142/S0217979213300077

and in the article by M. Agarwal and E. G. Mishchenko:

Long-range exchange interaction between magnetic impurities in graphene / Phys. Rev. B 95, 075411 (2017) DOI: 10.1103/PhysRevB.95.075411.

Thank you so much for pointing out the role of the RKKY interaction in Graphene, Dear Prof. Alexander T. Morchenko. And for pointing out the interesting paper:

Article Long-range exchange interaction between magnetic impurities ...

Dear Prof. Alexander T. Morchenko, thank you so much also for pointing out your review paper:

UNCONVENTIONAL AND EXOTIC MAGNETISM IN CARBON-BASED STRUCTURES AND RELATED MATERIALS

Article UNCONVENTIONAL AND EXOTIC MAGNETISM IN CARBON-BASED STRUCTUR...

You clearly and pedagogically establish the different magnetic interactions in table 3, so the RKKY is still an itinerant model but with smaller Curie temperature.

Thank you so much for following Dear Prof. Alaa Ali

The RKKY interaction theory is applicable to dilute solid solution of magnetic atoms in a nonmagnetic metal crystal. It is the interaction between the magnetic moments of two impurity magnetic ions via conduction electron giving rise to magnetic behavior. This interaction has been studied in various systems of condensed matter physics; such as spinglass, semiconductor, semimetal, quasicrystal, quantum dots, silicene, topological insulator and graphene.

An important inclusion of the RKKY interaction is given by the Anderson lattice.

Thank you so much for your answer, Prof. Snehadri Bihari Ota, concerning the interesting application of RKKY interaction to nonmagnetic metals with dilute solutions of magnetic atoms. A very important point for the applications in solid-state physics.

In the following paper, the magnetic ordering induced by the RKKY interaction is nicely explained by considering changes in the local geometry of the Fermi surface.

In concrete, the helicity vector is expected to be determined by the small diameter of the FS.

For the analysis, the density-density correlation function is used.

Article Spatial Correlation of Conduction Electrons in Metal with Co...

In the study of the RKKY interaction order becomes important.

A simple way to see the differences between short and large ordering is using an Ising model in a 2D/3D lattice.

The differences have been studied in the following works:

Article Relations between Short Range and Long Range Ising models

Moreover, it was found that an effective long-range interaction is realized among spins in systems where the elastic interaction causes the ordering of the spins.

In such systems is generally expected both long-range and short-range interactions to exist:

Article Crossover between a Short-range and a Long-range Ising model

What would be the role of the RKKY interaction ordering if we suppose the system is a metallic spin glass?

Spin glasses retain high entropy even at quite low temperatures. One example is Mn-doped in metals as an impurity.

Mn atoms interact with other Mn so (that is an impurity atom itself) via RKKY interaction Jij(r)∼ cos(2 kF r)/(kF r)3

Because of the oscillation, the interactions remain random.

Chapter The Ising Model: Brief Introduction and Its Application

RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction describes an interaction between two localized spins, mediated by conduction electrons. It is an oscillatory function of the distance between the two localized spins. Thus it can be both positive and negative, describing both ferromagnetic and antiferromagnetic interactions. It is an indirect exchange interaction and results from second order effects of s(p)-d(f) interaction in magnetic metals and semiconductors. Indirect interaction between two nuclear spins in a metal was first discussed by Ruderman and Kittel [1], treating the electron-nuclear hyperfine interaction in second order. Later, it was extended to localized spins in transition metals and alloys by Kasuya [2] and Yosida [3], hence the name RKKY. In addition to spin, these interactions could involve orbital and dipolar interactions as well [4-6].

[1]Ruderman, M. A.; Kittel, C. (1954). "Indirect Exchange Coupling of Nuclear Magnetic Moments by Conduction Electrons". Physical Review. 96: 99. doi:10.1103/PhysRev.96.99.

[2]Kasuya, Tadao (1956). "A Theory of Metallic Ferro- and Antiferromagnetism on Zener's Model". Progress of Theoretical Physics. 16: 45.. doi:10.1143/PTP.16.45.

[3]Yosida, Kei (1957). "Magnetic Properties of Cu-Mn Alloys". Physical Review. 106 (5): 893. doi:10.1103/PhysRev.106.893.

[4]. Gouri S. Tripathi (1985), Many-body theory of indirect nuclear interactions, Phys. Rev. B 31, 5143

[5]. Gouri S Tripathi (1986), Theory of magnetic susceptibility of Bloch electrons: Effect of localized magnetic moments, Physics Letters A 115 (4), 169-172

[6]. Gouri S. Tripathi (1987), Theory of magnetic susceptibility of Bloch electrons in the presence of localized magnetic moments, Phys. Rev. B 35, 5247

Thank you so much for your clear explanation and the references, Prof. Gouri S. Tripathi

Particularly, those using the Green functions technique with the RKKY interaction:

Article Many-body theory of indirect nuclear interactions

Article Theory of magnetic susceptibility of Bloch electrons: Effect...

Article Theory of magnetic susceptibility of Bloch electrons in the ...

Nice discussion

Thank you so much, Dear Bahram Kalhor.

RKKY interaction is one of the most powerful tools to describe complex interactions in solid-state physics, altogether with the sp-d exchange interaction and the spin-orbit interaction. All they are related to spins.

There are several Green function approaches to the RKKY interaction, one is a new one:

Article Exact Green's function approach to RKKY interactions

Another one, more textbook type according to the authors:

Article RKKY interaction in framework of T=0 Green function method

Thanking you for the references

My pleasure, Dr. Snehadri Bihari Ota.

A nice book to mention in this thread:

Rare Earth Magnetism: Structures and Excitations by J. Jensen and A. Mackintosh. Clarendon Press, Oxford   1991

An interesting academic discussion of the difference/similitudes between RKKY and Kondo mechanisms is given in the following external link:

https://physics.stackexchange.com/questions/247205/difference-between-ruderman-kittel-kasuya-yosida-rkky-interaction-and-kondo-ef

Both phenomena have the same origin, the screening of impurity by conductions electrons.

The following thread is relevant to this one:

https://www.researchgate.net/post/Could-you-please-explain-what-is-the-double-exchange-mechanism-in-multiferroics-RMn2O5

The following thread is related to RKKY using ab initio methods, I consider it useful and relevant:

https://www.researchgate.net/post/How_can_I_determine_the_type_of_exchange_interaction_of_compounds_from_the_Projected_Bandstructure_and_DOS

The author refers to the following very useful paper:

Article Trends of exchange interactions in dilute magnetic semiconductors

ZhETF, Vol. 159, No. 4, 2021 (JETP, Vol. 132, No. 4, 2021) has been dedicated to the 90th birthday of the theoretical physicist, Prof. Igor Ekhilievich Dzyaloshinskii, the creator of the antisymmetric exchange.

http://jetp.ac.ru/cgi-bin/e/index/r/159/4?a=list

https://en.wikipedia.org/wiki/Antisymmetric_exchange

I believe that the following information is relevant to this thread topic, however since it lacks a CC license, I will just point directly to the external links:

http://sciencewise.info/definitions/RKKY_interaction_by_Vadim_Cheianov

http://sciencewise.info/ontology/RKKY_interaction

Thank you for the post, Dr. Esteban Rodríguez Torres

The "secret in the RKKY interaction" is the indirect exchange mechanism, it opens a window for new physical phenomena, which do not happen in the direct exchange process. Nothing weird there, just it takes time to understand by the human brain.

Best Regards.

The following open access book contains some topics which are related to this thread:

Book Magnetism and Accelerator-Based Light Sources Proceedings of...

The following paper is worth mentioning in this thread:

Article Note on RKKY interactions in nearly-free electron systems

Dear Doctor

"The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction has been extended to the case when an external magnetic field is taken into account. It has been shown that the RKKY Hamiltonian should contain the Zeeman-like term in which the effective gyromagnetic factor occurs. This effective gyromagnetic factor contains a correction term which is linearly dependent on the contact potential between the localized spins and conduction electrons."

"Ruderman-Kittel-KasuyaYosida (RKKY) interaction, an indirect exchange interaction between two magnetic impurities mediated by conduction electrons, may provide an alternative mechanism for the DM interaction. The strength of RKKY interaction, characterized by the range function, usually oscillates as a function of distance between magnetic impurities with the period determined by the Fermi level, the effective mass of conduction electrons, and other material-dependent parameters ."

Dear Doctor

Go To

Electric field control of RKKY coupling through solid-state ionics

By

Maria Ameziane📷

;Roy Rosenkamp📷

;Lukáš Flajšman📷

;Sebastiaan van Dijken📷

Rhodri Mansell

Appl. Phys. Lett. 122, 232401 (2023)

https://doi.org/10.1063/5.0145144

"Placing a suitable spacer layer between two magnetic layers can lead to an interaction between the magnetic layers known as Ruderman–Kittel–Kasuya–Yosida (RKKY) coupling. Controlling RKKY coupling, particularly the ability to switch between ferromagnetic and antiferromagnetic coupling, would enable novel magnetic data storage devices. By combining solid-state Li ion battery technology with an out-of-plane magnetized Co/Pt-based stack coupled through a Ru interlayer, we investigate the effects of the insertion of Li ions on the magnetic properties of the stack. The RKKY coupling and its voltage dependence are measured as a function of the Ru interlayer thickness, along with the effects of repeated voltage cycling. The Li ions both change the amplitude of the RKKY coupling and its phase, leading to the ability to switch the RKKY coupling between ferromagnetic and antiferromagnetic with applied voltages."

I can share a recent publication, which to some extent relates to the topic under discussion: Features of Electrical and Magnetic Properties and Curie Point Behavior in Nanocomposites Based on Cd3As2 and MnAs_Bulletin of the Russian Academy of Sciences: Physics, 2023, Vol. 87, Suppl. 1, pp. S122-S132 (by M.H.Al-Onaizan, A.I.Ril’, A.N.Semin, N.A.Yudanov, M.A.Nemirovich and A.T.Morchenko), DOI: 10.3103/S1062873823704506.

Further work in this direction concerns the production of film nanostructures with such composition, in which both a smaller size of ferromagnetic particles and their more uniform distribution in size and volume of the composite will be achieved.

Any suggestions for the development of work in the direction of methods for obtaining and applying such materials, setting up new experiments for their research and interpretation of the results obtained are welcome.

Dear Profs. Alexander T. Morchenko and Sundus F Hantoosh thank you so much for your posts.

Prof. Alexander T. Morchenko thank you for the proposal as well.

Best Regards